Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.3% → 99.7%

Time: 5.6s

Alternatives: 12

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-273} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-273) (not (<= t_0 0.0))) t_0 (- (- z) (* z (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-273) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-273)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-273) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-273) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-273) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-273) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-273], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -2e-273 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -2e-273 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 12.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 96.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 96.8%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 99.9%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 99.9%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 99.9%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 99.9%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 99.9%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. unsub-neg 99.9%

         \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z}{y}} \]

      3. mul-1-neg 99.9%

         \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z}{y} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
   9. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(-z\right) + \left(-\frac{x \cdot z}{y}\right)} \]

      2. distribute-neg-out 99.9%

         \[\leadsto \color{blue}{-\left(z + \frac{x \cdot z}{y}\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]

      4. *-commutative 100.0%

         \[\leadsto -\left(z + \color{blue}{z \cdot \frac{x}{y}}\right) \]

   10. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{-\left(z + z \cdot \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-273} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- z) (* z (/ x y)))))
   (if (<= y -1.85e+112)
     t_0
     (if (<= y -2.05e+35)
       (+ x y)
       (if (<= y -6.5e-25)
         t_0
         (if (<= y 4.1e-100)
           (+ x y)
           (if (<= y 4.4e+15)
             (- (- z) (/ (* x z) y))
             (if (<= y 4.2e+47) (+ x y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -z - (z * (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_0;
	} else if (y <= -2.05e+35) {
		tmp = x + y;
	} else if (y <= -6.5e-25) {
		tmp = t_0;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 4.4e+15) {
		tmp = -z - ((x * z) / y);
	} else if (y <= 4.2e+47) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z - (z * (x / y))
    if (y <= (-1.85d+112)) then
        tmp = t_0
    else if (y <= (-2.05d+35)) then
        tmp = x + y
    else if (y <= (-6.5d-25)) then
        tmp = t_0
    else if (y <= 4.1d-100) then
        tmp = x + y
    else if (y <= 4.4d+15) then
        tmp = -z - ((x * z) / y)
    else if (y <= 4.2d+47) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z - (z * (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_0;
	} else if (y <= -2.05e+35) {
		tmp = x + y;
	} else if (y <= -6.5e-25) {
		tmp = t_0;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 4.4e+15) {
		tmp = -z - ((x * z) / y);
	} else if (y <= 4.2e+47) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z - (z * (x / y))
	tmp = 0
	if y <= -1.85e+112:
		tmp = t_0
	elif y <= -2.05e+35:
		tmp = x + y
	elif y <= -6.5e-25:
		tmp = t_0
	elif y <= 4.1e-100:
		tmp = x + y
	elif y <= 4.4e+15:
		tmp = -z - ((x * z) / y)
	elif y <= 4.2e+47:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) - Float64(z * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t_0;
	elseif (y <= -2.05e+35)
		tmp = Float64(x + y);
	elseif (y <= -6.5e-25)
		tmp = t_0;
	elseif (y <= 4.1e-100)
		tmp = Float64(x + y);
	elseif (y <= 4.4e+15)
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	elseif (y <= 4.2e+47)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z - (z * (x / y));
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t_0;
	elseif (y <= -2.05e+35)
		tmp = x + y;
	elseif (y <= -6.5e-25)
		tmp = t_0;
	elseif (y <= 4.1e-100)
		tmp = x + y;
	elseif (y <= 4.4e+15)
		tmp = -z - ((x * z) / y);
	elseif (y <= 4.2e+47)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+112], t$95$0, If[LessEqual[y, -2.05e+35], N[(x + y), $MachinePrecision], If[LessEqual[y, -6.5e-25], t$95$0, If[LessEqual[y, 4.1e-100], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.4e+15], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+47], N[(x + y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000002e112 or -2.0499999999999999e35 < y < -6.5e-25 or 4.2e47 < y

   1. Initial program 72.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.2%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 85.2%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 85.2%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 85.2%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 85.2%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around inf 82.2%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 82.2%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. unsub-neg 82.2%

         \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z}{y}} \]

      3. mul-1-neg 82.2%

         \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z}{y} \]

   8. Simplified 82.2%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
   9. Step-by-step derivation

      1. sub-neg 82.2%

         \[\leadsto \color{blue}{\left(-z\right) + \left(-\frac{x \cdot z}{y}\right)} \]

      2. distribute-neg-out 82.2%

         \[\leadsto \color{blue}{-\left(z + \frac{x \cdot z}{y}\right)} \]

      3. associate-*l/ 85.2%

         \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]

      4. *-commutative 85.2%

         \[\leadsto -\left(z + \color{blue}{z \cdot \frac{x}{y}}\right) \]

   10. Applied egg-rr 85.2%

       \[\leadsto \color{blue}{-\left(z + z \cdot \frac{x}{y}\right)} \]

   if -1.85000000000000002e112 < y < -2.0499999999999999e35 or -6.5e-25 < y < 4.0999999999999999e-100 or 4.4e15 < y < 4.2e47

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 83.8%

      \[\leadsto \color{blue}{y + x} \]

   if 4.0999999999999999e-100 < y < 4.4e15

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 67.8%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 67.8%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 67.8%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 67.8%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around inf 75.9%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 75.9%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. unsub-neg 75.9%

         \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z}{y}} \]

      3. mul-1-neg 75.9%

         \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z}{y} \]

   8. Simplified 75.9%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- z) (* z (/ x y)))))
   (if (<= y -1.8e+109)
     t_0
     (if (<= y -7e+35)
       (+ x y)
       (if (<= y -1.35e-24)
         t_0
         (if (<= y 4.1e-100)
           (+ x y)
           (if (<= y 1.15e+17)
             (/ (* z (+ x y)) (- y))
             (if (<= y 4.2e+47) (+ x y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -z - (z * (x / y));
	double tmp;
	if (y <= -1.8e+109) {
		tmp = t_0;
	} else if (y <= -7e+35) {
		tmp = x + y;
	} else if (y <= -1.35e-24) {
		tmp = t_0;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.15e+17) {
		tmp = (z * (x + y)) / -y;
	} else if (y <= 4.2e+47) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z - (z * (x / y))
    if (y <= (-1.8d+109)) then
        tmp = t_0
    else if (y <= (-7d+35)) then
        tmp = x + y
    else if (y <= (-1.35d-24)) then
        tmp = t_0
    else if (y <= 4.1d-100) then
        tmp = x + y
    else if (y <= 1.15d+17) then
        tmp = (z * (x + y)) / -y
    else if (y <= 4.2d+47) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z - (z * (x / y));
	double tmp;
	if (y <= -1.8e+109) {
		tmp = t_0;
	} else if (y <= -7e+35) {
		tmp = x + y;
	} else if (y <= -1.35e-24) {
		tmp = t_0;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.15e+17) {
		tmp = (z * (x + y)) / -y;
	} else if (y <= 4.2e+47) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z - (z * (x / y))
	tmp = 0
	if y <= -1.8e+109:
		tmp = t_0
	elif y <= -7e+35:
		tmp = x + y
	elif y <= -1.35e-24:
		tmp = t_0
	elif y <= 4.1e-100:
		tmp = x + y
	elif y <= 1.15e+17:
		tmp = (z * (x + y)) / -y
	elif y <= 4.2e+47:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) - Float64(z * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.8e+109)
		tmp = t_0;
	elseif (y <= -7e+35)
		tmp = Float64(x + y);
	elseif (y <= -1.35e-24)
		tmp = t_0;
	elseif (y <= 4.1e-100)
		tmp = Float64(x + y);
	elseif (y <= 1.15e+17)
		tmp = Float64(Float64(z * Float64(x + y)) / Float64(-y));
	elseif (y <= 4.2e+47)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z - (z * (x / y));
	tmp = 0.0;
	if (y <= -1.8e+109)
		tmp = t_0;
	elseif (y <= -7e+35)
		tmp = x + y;
	elseif (y <= -1.35e-24)
		tmp = t_0;
	elseif (y <= 4.1e-100)
		tmp = x + y;
	elseif (y <= 1.15e+17)
		tmp = (z * (x + y)) / -y;
	elseif (y <= 4.2e+47)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+109], t$95$0, If[LessEqual[y, -7e+35], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.35e-24], t$95$0, If[LessEqual[y, 4.1e-100], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.15e+17], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 4.2e+47], N[(x + y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e109 or -7.0000000000000001e35 < y < -1.35000000000000003e-24 or 4.2e47 < y

   1. Initial program 72.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.2%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 85.2%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 85.2%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 85.2%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 85.2%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around inf 82.2%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 82.2%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. unsub-neg 82.2%

         \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z}{y}} \]

      3. mul-1-neg 82.2%

         \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z}{y} \]

   8. Simplified 82.2%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
   9. Step-by-step derivation

      1. sub-neg 82.2%

         \[\leadsto \color{blue}{\left(-z\right) + \left(-\frac{x \cdot z}{y}\right)} \]

      2. distribute-neg-out 82.2%

         \[\leadsto \color{blue}{-\left(z + \frac{x \cdot z}{y}\right)} \]

      3. associate-*l/ 85.2%

         \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]

      4. *-commutative 85.2%

         \[\leadsto -\left(z + \color{blue}{z \cdot \frac{x}{y}}\right) \]

   10. Applied egg-rr 85.2%

       \[\leadsto \color{blue}{-\left(z + z \cdot \frac{x}{y}\right)} \]

   if -1.8e109 < y < -7.0000000000000001e35 or -1.35000000000000003e-24 < y < 4.0999999999999999e-100 or 1.15e17 < y < 4.2e47

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 83.8%

      \[\leadsto \color{blue}{y + x} \]

   if 4.0999999999999999e-100 < y < 1.15e17

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. +-commutative 72.1%

         \[\leadsto -\frac{z \cdot \color{blue}{\left(y + x\right)}}{y} \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{-\frac{z \cdot \left(y + x\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+110} \lor \neg \left(y \leq -6.2 \cdot 10^{+34}\right) \land \left(y \leq -7.5 \cdot 10^{-25} \lor \neg \left(y \leq 8.8 \cdot 10^{-89}\right)\right):\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+110)
         (and (not (<= y -6.2e+34)) (or (<= y -7.5e-25) (not (<= y 8.8e-89)))))
   (- (- z) (* z (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+110) || (!(y <= -6.2e+34) && ((y <= -7.5e-25) || !(y <= 8.8e-89)))) {
		tmp = -z - (z * (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.8d+110)) .or. (.not. (y <= (-6.2d+34))) .and. (y <= (-7.5d-25)) .or. (.not. (y <= 8.8d-89))) then
        tmp = -z - (z * (x / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+110) || (!(y <= -6.2e+34) && ((y <= -7.5e-25) || !(y <= 8.8e-89)))) {
		tmp = -z - (z * (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+110) or (not (y <= -6.2e+34) and ((y <= -7.5e-25) or not (y <= 8.8e-89))):
		tmp = -z - (z * (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+110) || (!(y <= -6.2e+34) && ((y <= -7.5e-25) || !(y <= 8.8e-89))))
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+110) || (~((y <= -6.2e+34)) && ((y <= -7.5e-25) || ~((y <= 8.8e-89)))))
		tmp = -z - (z * (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+110], And[N[Not[LessEqual[y, -6.2e+34]], $MachinePrecision], Or[LessEqual[y, -7.5e-25], N[Not[LessEqual[y, 8.8e-89]], $MachinePrecision]]]], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999998e110 or -6.19999999999999955e34 < y < -7.49999999999999989e-25 or 8.80000000000000048e-89 < y

   1. Initial program 79.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 68.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.4%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 78.2%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 78.2%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 78.2%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 78.2%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around inf 76.6%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 76.6%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. unsub-neg 76.6%

         \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z}{y}} \]

      3. mul-1-neg 76.6%

         \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z}{y} \]

   8. Simplified 76.6%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
   9. Step-by-step derivation

      1. sub-neg 76.6%

         \[\leadsto \color{blue}{\left(-z\right) + \left(-\frac{x \cdot z}{y}\right)} \]

      2. distribute-neg-out 76.6%

         \[\leadsto \color{blue}{-\left(z + \frac{x \cdot z}{y}\right)} \]

      3. associate-*l/ 78.2%

         \[\leadsto -\left(z + \color{blue}{\frac{x}{y} \cdot z}\right) \]

      4. *-commutative 78.2%

         \[\leadsto -\left(z + \color{blue}{z \cdot \frac{x}{y}}\right) \]

   10. Applied egg-rr 78.2%

       \[\leadsto \color{blue}{-\left(z + z \cdot \frac{x}{y}\right)} \]

   if -1.7999999999999998e110 < y < -6.19999999999999955e34 or -7.49999999999999989e-25 < y < 8.80000000000000048e-89

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 83.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 83.0%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+110} \lor \neg \left(y \leq -6.2 \cdot 10^{+34}\right) \land \left(y \leq -7.5 \cdot 10^{-25} \lor \neg \left(y \leq 8.8 \cdot 10^{-89}\right)\right):\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+113} \lor \neg \left(y \leq 2.4 \cdot 10^{+37} \lor \neg \left(y \leq 3.6 \cdot 10^{+72}\right) \land y \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e+113)
         (not (or (<= y 2.4e+37) (and (not (<= y 3.6e+72)) (<= y 1.65e+125)))))
   (- z)
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+113) || !((y <= 2.4e+37) || (!(y <= 3.6e+72) && (y <= 1.65e+125)))) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.85d+113)) .or. (.not. (y <= 2.4d+37) .or. (.not. (y <= 3.6d+72)) .and. (y <= 1.65d+125))) then
        tmp = -z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+113) || !((y <= 2.4e+37) || (!(y <= 3.6e+72) && (y <= 1.65e+125)))) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e+113) or not ((y <= 2.4e+37) or (not (y <= 3.6e+72) and (y <= 1.65e+125))):
		tmp = -z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e+113) || !((y <= 2.4e+37) || (!(y <= 3.6e+72) && (y <= 1.65e+125))))
		tmp = Float64(-z);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.85e+113) || ~(((y <= 2.4e+37) || (~((y <= 3.6e+72)) && (y <= 1.65e+125)))))
		tmp = -z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e+113], N[Not[Or[LessEqual[y, 2.4e+37], And[N[Not[LessEqual[y, 3.6e+72]], $MachinePrecision], LessEqual[y, 1.65e+125]]]], $MachinePrecision]], (-z), N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8499999999999999e113 or 2.4e37 < y < 3.60000000000000035e72 or 1.65000000000000003e125 < y

   1. Initial program 68.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.2%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.2%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 79.2%

      \[\leadsto \color{blue}{-z} \]

   if -1.8499999999999999e113 < y < 2.4e37 or 3.60000000000000035e72 < y < 1.65000000000000003e125

   1. Initial program 98.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.9%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+113} \lor \neg \left(y \leq 2.4 \cdot 10^{+37} \lor \neg \left(y \leq 3.6 \cdot 10^{+72}\right) \land y \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.6e+109)
   (- z)
   (if (<= y 4.1e-100)
     (+ x y)
     (if (<= y 1.2e+14) (/ (* x z) (- y)) (if (<= y 4e+48) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.6e+109) {
		tmp = -z;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.2e+14) {
		tmp = (x * z) / -y;
	} else if (y <= 4e+48) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.6d+109)) then
        tmp = -z
    else if (y <= 4.1d-100) then
        tmp = x + y
    else if (y <= 1.2d+14) then
        tmp = (x * z) / -y
    else if (y <= 4d+48) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.6e+109) {
		tmp = -z;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.2e+14) {
		tmp = (x * z) / -y;
	} else if (y <= 4e+48) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.6e+109:
		tmp = -z
	elif y <= 4.1e-100:
		tmp = x + y
	elif y <= 1.2e+14:
		tmp = (x * z) / -y
	elif y <= 4e+48:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.6e+109)
		tmp = Float64(-z);
	elseif (y <= 4.1e-100)
		tmp = Float64(x + y);
	elseif (y <= 1.2e+14)
		tmp = Float64(Float64(x * z) / Float64(-y));
	elseif (y <= 4e+48)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.6e+109)
		tmp = -z;
	elseif (y <= 4.1e-100)
		tmp = x + y;
	elseif (y <= 1.2e+14)
		tmp = (x * z) / -y;
	elseif (y <= 4e+48)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.6e+109], (-z), If[LessEqual[y, 4.1e-100], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.2e+14], N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 4e+48], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000021e109 or 4.00000000000000018e48 < y

   1. Initial program 69.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.4%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 73.4%

      \[\leadsto \color{blue}{-z} \]

   if -4.60000000000000021e109 < y < 4.0999999999999999e-100 or 1.2e14 < y < 4.00000000000000018e48

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.4%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.4%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{y + x} \]

   if 4.0999999999999999e-100 < y < 1.2e14

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 67.8%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 67.8%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 67.8%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 67.8%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around 0 52.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 52.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} \]

      2. associate-*r* 52.4%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot x\right) \cdot z}}{y} \]

      3. mul-1-neg 52.4%

         \[\leadsto \frac{\color{blue}{\left(-x\right)} \cdot z}{y} \]

   8. Simplified 52.4%

      \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+110)
   (- z)
   (if (<= y 4.1e-100)
     (+ x y)
     (if (<= y 1.02e+14)
       (* x (/ z (- y)))
       (if (<= y 2.25e+48) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+110) {
		tmp = -z;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.02e+14) {
		tmp = x * (z / -y);
	} else if (y <= 2.25e+48) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.5d+110)) then
        tmp = -z
    else if (y <= 4.1d-100) then
        tmp = x + y
    else if (y <= 1.02d+14) then
        tmp = x * (z / -y)
    else if (y <= 2.25d+48) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+110) {
		tmp = -z;
	} else if (y <= 4.1e-100) {
		tmp = x + y;
	} else if (y <= 1.02e+14) {
		tmp = x * (z / -y);
	} else if (y <= 2.25e+48) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e+110:
		tmp = -z
	elif y <= 4.1e-100:
		tmp = x + y
	elif y <= 1.02e+14:
		tmp = x * (z / -y)
	elif y <= 2.25e+48:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+110)
		tmp = Float64(-z);
	elseif (y <= 4.1e-100)
		tmp = Float64(x + y);
	elseif (y <= 1.02e+14)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 2.25e+48)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e+110)
		tmp = -z;
	elseif (y <= 4.1e-100)
		tmp = x + y;
	elseif (y <= 1.02e+14)
		tmp = x * (z / -y);
	elseif (y <= 2.25e+48)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+110], (-z), If[LessEqual[y, 4.1e-100], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.02e+14], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+48], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999996e110 or 2.24999999999999998e48 < y

   1. Initial program 69.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.4%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 73.4%

      \[\leadsto \color{blue}{-z} \]

   if -5.49999999999999996e110 < y < 4.0999999999999999e-100 or 1.02e14 < y < 2.24999999999999998e48

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.4%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.4%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{y + x} \]

   if 4.0999999999999999e-100 < y < 1.02e14

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 67.8%

         \[\leadsto -\color{blue}{z \cdot \frac{x + y}{y}} \]

      3. distribute-rgt-neg-in 67.8%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{x + y}{y}\right)} \]

      4. distribute-neg-frac2 67.8%

         \[\leadsto z \cdot \color{blue}{\frac{x + y}{-y}} \]

      5. +-commutative 67.8%

         \[\leadsto z \cdot \frac{\color{blue}{y + x}}{-y} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]

   6. Taylor expanded in y around 0 52.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.4%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{y}} \]

      2. associate-/l* 52.4%

         \[\leadsto -\color{blue}{x \cdot \frac{z}{y}} \]

      3. distribute-rgt-neg-in 52.4%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{z}{y}\right)} \]

      4. mul-1-neg 52.4%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]

      5. associate-*r/ 52.4%

         \[\leadsto x \cdot \color{blue}{\frac{-1 \cdot z}{y}} \]

      6. mul-1-neg 52.4%

         \[\leadsto x \cdot \frac{\color{blue}{-z}}{y} \]

   8. Simplified 52.4%

      \[\leadsto \color{blue}{x \cdot \frac{-z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-30}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+109)
   (- z)
   (if (<= y 1.55e-122) x (if (<= y 2.4e-30) y (if (<= y 2.1e-28) x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+109) {
		tmp = -z;
	} else if (y <= 1.55e-122) {
		tmp = x;
	} else if (y <= 2.4e-30) {
		tmp = y;
	} else if (y <= 2.1e-28) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.8d+109)) then
        tmp = -z
    else if (y <= 1.55d-122) then
        tmp = x
    else if (y <= 2.4d-30) then
        tmp = y
    else if (y <= 2.1d-28) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+109) {
		tmp = -z;
	} else if (y <= 1.55e-122) {
		tmp = x;
	} else if (y <= 2.4e-30) {
		tmp = y;
	} else if (y <= 2.1e-28) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e+109:
		tmp = -z
	elif y <= 1.55e-122:
		tmp = x
	elif y <= 2.4e-30:
		tmp = y
	elif y <= 2.1e-28:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+109)
		tmp = Float64(-z);
	elseif (y <= 1.55e-122)
		tmp = x;
	elseif (y <= 2.4e-30)
		tmp = y;
	elseif (y <= 2.1e-28)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.8e+109)
		tmp = -z;
	elseif (y <= 1.55e-122)
		tmp = x;
	elseif (y <= 2.4e-30)
		tmp = y;
	elseif (y <= 2.1e-28)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+109], (-z), If[LessEqual[y, 1.55e-122], x, If[LessEqual[y, 2.4e-30], y, If[LessEqual[y, 2.1e-28], x, (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e109 or 2.10000000000000006e-28 < y

   1. Initial program 74.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.2%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{-z} \]

   if -1.8e109 < y < 1.5499999999999999e-122 or 2.39999999999999985e-30 < y < 2.10000000000000006e-28

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.1%

      \[\leadsto \color{blue}{x} \]

   if 1.5499999999999999e-122 < y < 2.39999999999999985e-30

   1. Initial program 99.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 40.7%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around 0 32.5%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+175}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -4.5e+109)
     (- z)
     (if (<= y 4.5e-37) (/ x t_0) (if (<= y 5.1e+175) (/ y t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -4.5e+109) {
		tmp = -z;
	} else if (y <= 4.5e-37) {
		tmp = x / t_0;
	} else if (y <= 5.1e+175) {
		tmp = y / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-4.5d+109)) then
        tmp = -z
    else if (y <= 4.5d-37) then
        tmp = x / t_0
    else if (y <= 5.1d+175) then
        tmp = y / t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -4.5e+109) {
		tmp = -z;
	} else if (y <= 4.5e-37) {
		tmp = x / t_0;
	} else if (y <= 5.1e+175) {
		tmp = y / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -4.5e+109:
		tmp = -z
	elif y <= 4.5e-37:
		tmp = x / t_0
	elif y <= 5.1e+175:
		tmp = y / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -4.5e+109)
		tmp = Float64(-z);
	elseif (y <= 4.5e-37)
		tmp = Float64(x / t_0);
	elseif (y <= 5.1e+175)
		tmp = Float64(y / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -4.5e+109)
		tmp = -z;
	elseif (y <= 4.5e-37)
		tmp = x / t_0;
	elseif (y <= 5.1e+175)
		tmp = y / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+109], (-z), If[LessEqual[y, 4.5e-37], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 5.1e+175], N[(y / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999996e109 or 5.10000000000000007e175 < y

   1. Initial program 61.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 84.6%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 84.6%

      \[\leadsto \color{blue}{-z} \]

   if -4.4999999999999996e109 < y < 4.5000000000000004e-37

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   if 4.5000000000000004e-37 < y < 5.10000000000000007e175

   1. Initial program 93.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 57.1%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+114} \lor \neg \left(y \leq 2.4 \cdot 10^{+48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+114) (not (<= y 2.4e+48))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+114) || !(y <= 2.4e+48)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.2d+114)) .or. (.not. (y <= 2.4d+48))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+114) || !(y <= 2.4e+48)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+114) or not (y <= 2.4e+48):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+114) || !(y <= 2.4e+48))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+114) || ~((y <= 2.4e+48)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+114], N[Not[LessEqual[y, 2.4e+48]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000001e114 or 2.4000000000000001e48 < y

   1. Initial program 69.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.4%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 73.4%

      \[\leadsto \color{blue}{-z} \]

   if -6.2000000000000001e114 < y < 2.4000000000000001e48

   1. Initial program 99.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.4%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+114} \lor \neg \left(y \leq 2.4 \cdot 10^{+48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-168}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-148) x (if (<= x 3.8e-168) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-148) {
		tmp = x;
	} else if (x <= 3.8e-168) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d-148)) then
        tmp = x
    else if (x <= 3.8d-168) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-148) {
		tmp = x;
	} else if (x <= 3.8e-168) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-148:
		tmp = x
	elif x <= 3.8e-168:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-148)
		tmp = x;
	elseif (x <= 3.8e-168)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-148)
		tmp = x;
	elseif (x <= 3.8e-168)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-148], x, If[LessEqual[x, 3.8e-168], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e-148 or 3.8e-168 < x

   1. Initial program 91.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 47.7%

      \[\leadsto \color{blue}{x} \]

   if -2.1e-148 < x < 3.8e-168

   1. Initial program 84.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 70.1%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around 0 38.5%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 35.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 89.7%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 39.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))